To find the factored form of the quadratic expression 3x² + 5x + 2, we will first look for two numbers that multiply to give us the product of the coefficient of x² (which is 3) and the constant term (which is 2), resulting in 3 * 2 = 6. We also need these two numbers to add up to the coefficient of x (which is 5).
The numbers that satisfy these conditions are 3 and 2, since 3 * 2 = 6 and 3 + 2 = 5.
Next, we can rewrite the middle term of the quadratic using these two numbers:
3x² + 3x + 2x + 2
Now, we can group the terms:
(3x² + 3x) + (2x + 2)
Factoring each group gives us:
3x(x + 1) + 2(x + 1)
We can now factor out the common term (x + 1):
(3x + 2)(x + 1)
Thus, the factored form of 3x² + 5x + 2 is (3x + 2)(x + 1).